Existing fuzzy controller designs are based on the Compositional Rule of Inference (CRI) for approximate reasoning of L. A. Zadeh. This approach applies the notion of membership function to measure the compatibility of fuzzy linguistic categories, such as HIGH, LOW etc., with the crisp and deterministic values (usually measured, calculated or assigned) which are utilized to describe the state of the process variables and objects, such as TEMPERATURE, PRESSURE, etc. In this approach, the control rules (acquired from experts) are interpreted in the controller knowledge-base as fuzzy relations which are represented as fuzzy matrices. For multivariable processes these matrices become multi-dimensional. The inference and approximate reasoning procedure of the CRI is performed using the time-consuming Max-Min operations over these matrices. As a result the operation of the controller can handle slow and simple processes but may face difficulties to cope with real-time applications for fast and complex multivariable processes due to the huge computations required to implement their functionality. Another principal limitation on the CRI based fuzzy controllers is that they perform reasoning at the fuzzy data level (where the rules and membership functions are mapped into matrices) and can not perform reasoning at the level of fuzzy patterns as the human usually does in handling the real world situations. This makes it difficult to use these controllers to simulate the various functionalities of human thinking which usually manipulates patterns in the problem solving practice, not massive data processing. Another difficulty faced by the CRI based fuzzy controllers is that they are unable to generate scenarios and records to describe their behaviour in terms of the tasks and patterns they simulate in their operations so that they may be used to match the human behaviour involved in similar control tasks. This is due to the algorithmic rather than cognitive bases of the approximate reasoning procedure of the CRI employed in these controllers. The compatibility between the operation of fuzzy controller devices and the human thinking is an important issue required for enhancing the functional intelligence of these controllers and for simplifying the acquisition of the knowledge from experts which, in turn, shortens the time of application development.
Other relevant literature includes:
1) Rasmussen, Information processing and Human-Machine Interaction. An Approach to Cognitive Engineering. Noah-Holland, 1986.
2) Sultan, "A composition of binary and multivalued logic for the procedures organization of fuzzy expert systems," IEEE Proceedings on ISMVL, pp. 154-159, 1984.
3) Sultan, "Some considerations on systems organization for fuzzy information processing", in: Trapple L. (ed.), Cybernetics and system research, North-Holland, pp. 551-556, 1984.
4) L. Sultan, "A formal approach for the organization and implementation of fuzzy micro- processor module", Fuzzy Computing, pp. 201-221, 1988.
5) Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans Systems, Man and Cybernetics., vol. SMC-3, pp. 28-44, 1973.
6) L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning, I and II", Inform. Sci., vol. 8, pp. 199-249 and vol. 9, pp. 301-357, 1975.